Simple gate functions always follow a specific true table. The inputs and output "active states" has more to do with the application of the gate in the circuit.
Example;
A simple 74X00 NAND gate can to used as both an "AND type" function (2 high inputs = low out) or as a "OR type" function (either or both input low = high out), same gate, same truth table, just two different applications.
It helps if the designer of a logic circuit uses the convection of using signal names that have a bar over the top for active low state or no bar for a active high state. Again this has nothing to do with the chip's stated logic function but rather how it's being utilized in a specific circuit.
The whole concept of positive and negitive logic can be confusing to some but sticking to the device truth tables should generally help one figure it out in spite of the jargon used.
Lefty